Let `a_1 lt a_2lt a_3 ...a_lt1` `p_1gt p_2 gt ...p_n gt0` ; such that `p_1 + p_2+ p_3 + p_n= 1` . Also `F(x)=(p_1a_1^x+p_2a_2^x+...+p_nan^x)^(1/x)` Compute

Let a_1gt a_2gt a_3 ...a_gt1 p_1gt p_2 gt ...p_n gt0 ; such that p_1 + p_2+ p_3 + p_n= 1 . Also F(x)=(p_1a_1^x+p_2a_2^x+...+p_nan^x)^(1/x) Then lim x→∞F(x) equals

Let a_(1)gta_(2)gta_(3)gt...gta_(n)gt1. p_(1)gtp_(2)gtp_(3)gt...gtp_(n)gt0" such that "p_(1)+p_(2)+p_(3)+...+p_(n)=1. Also, F(x)=(p_(1)a_(1)^(x)+...p_(n)a_(n)^(x))^(1//x) . lim_(xtooo) F(x)" equals "

Let a_(1)gta_(2)gta_(3)gt...gta_(n)gt1. p_(1)gtp_(2)gtp_(3)gt...gtp_(n)gt0" such that "p_(1)+p_(2)+p_(3)+...+p_(n)=1. Also, F(x)=(p_(1)a_(1)^(x)+p_(n)a_(n)^(x))^(1//x) . lim_(xto0^(+)) F(x)" equals "

Let a_(1)gta_(2)gta_(3)gt...gta_(n)gt1. p_(1)gtp_(2)gtp_(3)gt...gtp_(n)gt0" such that "p_(1)+p_(2)+p_(3)+...+p_(n)=1. Also, F(x)=(p_(1)a_(1)^(x)+p_(n)a_(n)^(x))^(1//x) . lim_(xto0^(+)) F(x)" equals "

Let a_(1)gta_(2)gta_(3)gt...gta_(n)gt1. p_(1)gtp_(2)gtp_(3)gt...gtp_(n)gt0" such that "p_(1)+p_(2)+p_(3)+...+p_(n)=1. Also, F(x)=(p_(1)a_(1)^(x)+p_(n)a_(n)^(x))^(1//x) . lim_(xtooo) F(x)" equals "

Let a_(1)gta_(2)gta_(3)gt...gta_(n)gt1. p_(1)gtp_(2)gtp_(3)gt...gtp_(n)gt0" such that "p_(1)+p_(2)+p_(3)+...+p_(n)=1. Also, F(x)=(p_(1)a_(1)^(x)+p_(n)a_(n)^(x))^(1//x) . lim_(xtooo) F(x)" equals "

State whether (p_1 gt p_2 or p_2 gt p_1) for given mass of a gas ? .

(1 + x)^(n) = p_(0) + p_(1) x + p_(2) x^(2) + … + p_(n) x^(n) , then p_(0) + p_(3) + p_(6) + ….. =

For p(x)= 2 x^ 2 − 3 x + 1 , find p(0),p(1),p(-1)

statement 1: Let p_1,p_2,...,p_n and x be distinct real number such that (sum_(r=1)^(n-1)p_r^2)x^2+2(sum_(r=1)^(n-1)p_r p_(r+1))x+sum_(r=2)^n p_r^2 lt=0 then p_1,p_2,...,p_n are in G.P. and when a_1^2+a_2^2+a_3^2+...+a_n^2=0,a_1=a_2=a_3=...=a_n=0 Statement 2 : If p_2/p_1=p_3/p_2=....=p_n/p_(n-1), then p_1,p_2,...,p_n are in G.P.